Machine Learning Conservation Laws from Trajectories
Ziming Liu, Max Tegmark
Abstract
We present AI Poincaré, a machine learning algorithm for autodiscovering conserved quantities using trajectory data from unknown dynamical systems. We test it on five Hamiltonian systems, including the gravitational three-body problem, and find that it discovers not only all exactly conserved quantities, but also periodic orbits, phase transitions, and breakdown timescales for approximate conservation laws.
Topics & Concepts
Conservation lawConserved quantityTrajectoryHamiltonian (control theory)Classical mechanicsHamiltonian systemPhysicsGravitationDynamical systems theoryComputer scienceStatistical physicsMathematicsMathematical optimizationQuantum mechanicsComputational Physics and Python ApplicationsGamma-ray bursts and supernovaeGaussian Processes and Bayesian Inference